The simple interest earned by a certain amount of money varies jointly as the
rate of interest and the time (in years) that the money is invested. If $140 is
earned for the money invested at 7% for 5 years, how much is earned if the same
amount is invested at 8% for 3 years?
Solution:
So since this is a simple interest problem here is the formula we'll be working with:
I=PRT, where I is the interest earned, P is the investment, R is the interest rate and T is time.
We have two steps.
1) Find P given I, R, T.
$140 = (P)(7%)(5) =$400
2) Find I given P, R, T.
I= ($400)(8%)(3) =$96
A farming field can be ploughed by 6 tractors in 4 days. When 6 tractors work
together, each of them ploughs 120 hectares a day. If two of the tractors were
moved to another field, then the remaining 4 tractors could plough the same
field in 5 days. How many hectares a day would one tractor plough then?
Solution:
If each of 6 tractors ploughed 120 hectares a day and they finished the work
in 4 days, then the whole field is: 120⋅6⋅4=720⋅4=2880 hectares. Let's suppose
that each of the four tractors ploughed x hectares a day. Therefore in 5 days
they ploughed
5⋅4⋅x=20⋅x hectares, which equals the area of the whole field, 2880 hectares.
So, we get 20x=2880
x=2880/20=144. Hence, each of the four tractors would plough 144 hectares a
day.
A triangle has a perimeter of 50. If 2 of its sides are equal and the third side is 5 more
than the equal sides, what is the length of the third side?
Be careful! The question requires the length of the third side.
The length of third side = 15 + 5 =20
Answer: The length of third side is 20
The diameter of a circular park is 98 m. Find the cost of fencing it at $4
per meter.
Circumference of the park is
= 2πr
= 2 (22/7) x 49
= 2 x 22 x 7
= 308 m
Cost for fencing is
= 308 x 4
= $1232
The angle of elevation of the top of the building at a distance of 50 m from
its foot on a horizontal plane is found to be 60°. Find the height of the
building.
Solution :
Draw a sketch.
Here, AB represents height of the building, BC represents distance of the
building from the point of observation.
In the right triangle ABC, the side which is opposite to the angle 60° is known
as opposite side (AB), the side which is opposite to 90° is called hypotenuse
side (AC) and the remaining side is called adjacent side (BC).
Now we need to find the length of the side AB.
tanθ = Opposite side/Adjacent side
tan60° = AB/BC
√3 = AB/50
√3 x 50 = AB
AB = 50√3
Approximate value of √3 is 1.732
AB = 50 (1.732)
AB = 86.6 m
So, the height of the building is 86.6 m.